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# Find the Missing Number in a sorted array

Given a list of n-1 integers and these integers are in the range of 1 to n. There are no duplicates in list. One of the integers is missing in the list. Write an efficient code to find the missing integer.
Examples:

Input : arr[] = [1, 2, 3, 4, 6, 7, 8]
Output : 5

Input : arr[] = [1, 2, 3, 4, 5, 6, 8, 9]
Output : 7

Naive approach: One Simple solution is to apply methods discussed for finding the missing element in an unsorted array.

Algorithm

• Create an empty hash table.
• Traverse through the given list of n-1 integers and insert each integer into the hash table.
• Traverse through the range of 1 to n and check whether each integer is present in the hash table or not.
• If any integer is not present in the hash table, then it is the missing integer.

Implementation

## C++

 `#include ``#include ` `using` `namespace` `std;` `int` `findMissingNumber(``int` `arr[], ``int` `n) {``    ``unordered_set<``int``> hashSet;` `    ``// Add all elements of array to hashset``    ``for` `(``int` `i = 0; i < n-1; i++) {``        ``hashSet.insert(arr[i]);``    ``}` `    ``// Check each integer from 1 to n``    ``for` `(``int` `i = 1; i <= n; i++) {``        ``// If integer is not in hashset, it is the missing integer``        ``if` `(hashSet.find(i) == hashSet.end()) {``            ``return` `i;``        ``}``    ``}` `    ``// If no integer is missing, return n+1``    ``return` `n+1;``}` `int` `main() {``    ``int` `arr[] = {1, 2, 4, 6, 3, 7, 8};``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``int` `missingNumber = findMissingNumber(arr, n);``    ``cout << ``"Missing number is: "` `<< missingNumber << endl;` `    ``return` `0;``}`

## Java

 `import` `java.util.HashSet;` `public` `class` `Main {``public` `static` `int` `findMissingNumber(``int``[] arr, ``int` `n) {``HashSet hashSet = ``new` `HashSet();``      ``// Add all elements of array to hashset``    ``for` `(``int` `i = ``0``; i < n-``1``; i++) {``        ``hashSet.add(arr[i]);``    ``}` `    ``// Check each integer from 1 to n``    ``for` `(``int` `i = ``1``; i <= n; i++) {``        ``// If integer is not in hashset, it is the missing integer``        ``if` `(!hashSet.contains(i)) {``            ``return` `i;``        ``}``    ``}` `    ``// If no integer is missing, return n+1``    ``return` `n+``1``;``}` `public` `static` `void` `main(String[] args) {``    ``int``[] arr = {``1``, ``2``, ``4``, ``6``, ``3``, ``7``, ``8``};``    ``int` `n = arr.length;` `    ``int` `missingNumber = findMissingNumber(arr, n);``    ``System.out.println(``"Missing number is: "` `+ missingNumber);``}``}`

## C#

 `using` `System;``using` `System.Collections.Generic;` `class` `Program``{``    ``static` `int` `FindMissingNumber(``int``[] arr, ``int` `n)``    ``{``        ``HashSet<``int``> hashSet = ``new` `HashSet<``int``>();` `        ``// Add all elements of array to hashset``        ``for` `(``int` `i = 0; i < n - 1; i++)``        ``{``            ``hashSet.Add(arr[i]);``        ``}` `        ``// Check each integer from 1 to n``        ``for` `(``int` `i = 1; i <= n; i++)``        ``{``            ``// If integer is not in hashset, it is the missing integer``            ``if` `(!hashSet.Contains(i))``            ``{``                ``return` `i;``            ``}``        ``}` `        ``// If no integer is missing, return n+1``        ``return` `n + 1;``    ``}` `    ``static` `void` `Main(``string``[] args)``    ``{``        ``int``[] arr = { 1, 2, 4, 6, 3, 7, 8 };``        ``int` `n = arr.Length;` `        ``int` `missingNumber = FindMissingNumber(arr, n);``        ``Console.WriteLine(``"Missing number is: "` `+ missingNumber);``    ``}``}`

## Python

 `def` `find_missing_number(arr):``    ``n ``=` `len``(arr) ``+` `1``    ``hash_set ``=` `set``(arr)` `    ``for` `i ``in` `range``(``1``, n):``        ``if` `i ``not` `in` `hash_set:``            ``return` `i` `    ``return` `n` `arr ``=` `[``1``, ``2``, ``4``, ``6``, ``3``, ``7``, ``8``]``missing_number ``=` `find_missing_number(arr)``print``(``"Missing number is:"``, missing_number)`

## Javascript

 `function` `findMissingNumber(arr, n) {``  ``let hashSet = ``new` `Set();` `  ``// Add all elements of array to hashset``  ``for` `(let i = 0; i < n - 1; i++) {``    ``hashSet.add(arr[i]);``  ``}` `  ``// Check each integer from 1 to n``  ``for` `(let i = 1; i <= n; i++) {``    ``// If integer is not in hashset, it is the missing integer``    ``if` `(!hashSet.has(i)) {``      ``return` `i;``    ``}``  ``}` `  ``// If no integer is missing, return n+1``  ``return` `n + 1;``}` `let arr = [1, 2, 4, 6, 3, 7, 8];``let n = arr.length;` `let missingNumber = findMissingNumber(arr, n);``console.log(``"Missing number is: "` `+ missingNumber);`

Output

`Missing number is: 5`

Time Complexity: O(n), where n is the length of given array
Auxiliary Space: O(n)

Efficient approach: It is based on the divide and conquer algorithm that we have seen in binary search, the concept behind this solution is that the elements appearing before the missing element will have ar[i] – i = 1 and those appearing after the missing element will have ar[i] – i = 2.

Below is the implementation of the above approach:

## C++

 `// A binary search based program to find the``// only missing number in a sorted array of``// distinct elements within limited range.``#include ``using` `namespace` `std;` `int` `search(``int` `ar[], ``int` `size)``{``    ``// Extreme cases``    ``if` `(ar[0] != 1)``        ``return` `1;``    ``if` `(ar[size - 1] != (size + 1))``        ``return` `size + 1;` `    ``int` `a = 0, b = size - 1;``    ``int` `mid;``    ``while` `((b - a) > 1) {``        ``mid = (a + b) / 2;``        ``if` `((ar[a] - a) != (ar[mid] - mid))``            ``b = mid;``        ``else` `if` `((ar[b] - b) != (ar[mid] - mid))``            ``a = mid;``    ``}``    ``return` `(ar[a] + 1);``}` `int` `main()``{``    ``int` `ar[] = { 1, 2, 3, 4, 5, 6, 8 };``    ``int` `size = ``sizeof``(ar) / ``sizeof``(ar[0]);``    ``cout << ``"Missing number:"` `<< search(ar, size);``}` `// This code is contributed by Pushpesh Raj`

## Java

 `// A binary search based program``// to find the only missing number``// in a sorted array of distinct``// elements within limited range.``import` `java.io.*;` `class` `GFG {``    ``static` `int` `search(``int` `ar[], ``int` `size)``    ``{``        ``// Extreme cases``        ``if` `(ar[``0``] != ``1``)``            ``return` `1``;``        ``if` `(ar[size - ``1``] != (size + ``1``))``            ``return` `size + ``1``;` `        ``int` `a = ``0``, b = size - ``1``;``        ``int` `mid = ``0``;``        ``while` `((b - a) > ``1``) {``            ``mid = (a + b) / ``2``;``            ``if` `((ar[a] - a) != (ar[mid] - mid))``                ``b = mid;``            ``else` `if` `((ar[b] - b) != (ar[mid] - mid))``                ``a = mid;``        ``}``        ``return` `(ar[a] + ``1``);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `ar[] = { ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``8` `};``        ``int` `size = ar.length;``        ``System.out.println(``"Missing number: "``                           ``+ search(ar, size));``    ``}``}` `// This code is contributed``// by inder_verma.`

## Python3

 `# A binary search based program to find``# the only missing number in a sorted``# in a sorted array of distinct elements``# within limited range`  `def` `search(ar, size):``   ``# Extreme cases``    ``if``(ar[``0``] !``=` `1``):``        ``return` `1``    ``if``(ar[size``-``1``] !``=` `(size``+``1``)):``        ``return` `size``+``1` `    ``a ``=` `0``    ``b ``=` `size ``-` `1``    ``mid ``=` `0``    ``while` `b > a ``+` `1``:``        ``mid ``=` `(a ``+` `b) ``/``/` `2``        ``if` `(ar[a] ``-` `a) !``=` `(ar[mid] ``-` `mid):``            ``b ``=` `mid``        ``elif` `(ar[b] ``-` `b) !``=` `(ar[mid] ``-` `mid):``            ``a ``=` `mid``    ``return` `ar[a] ``+` `1`  `# Driver Code``a ``=` `[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``8``]``n ``=` `len``(a)` `print``(``"Missing number:"``, search(a, n))` `# This code is contributed``# by Mohit Kumar`

## C#

 `// A binary search based program``// to find the only missing number``// in a sorted array of distinct``// elements within limited range.``using` `System;` `class` `GFG {``    ``static` `int` `search(``int``[] ar, ``int` `size)``    ``{``        ``// Extreme cases``        ``if` `(ar[0] != 1)``            ``return` `1;``        ``if` `(ar[size - 1] != (size + 1))``            ``return` `size + 1;` `        ``int` `a = 0, b = size - 1;``        ``int` `mid = 0;``        ``while` `((b - a) > 1) {``            ``mid = (a + b) / 2;``            ``if` `((ar[a] - a) != (ar[mid] - mid))``                ``b = mid;``            ``else` `if` `((ar[b] - b) != (ar[mid] - mid))``                ``a = mid;``        ``}``        ``return` `(ar[a] + 1);``    ``}` `    ``// Driver Code``    ``static` `public` `void` `Main(String[] args)``    ``{``        ``int``[] ar = { 1, 2, 3, 4, 5, 6, 8 };``        ``int` `size = ar.Length;``        ``Console.WriteLine(``"Missing number: "``                          ``+ search(ar, size));``    ``}``}` `// This code is contributed``// by Arnab Kundu`

## PHP

 ` 1)``    ``{``        ``\$mid` `= (int)((``\$a` `+ ``\$b``) / 2);``        ``if` `((``\$ar``[``\$a``] - ``\$a``) != (``\$ar``[``\$mid``] -``                                   ``\$mid``))``            ``\$b` `= ``\$mid``;``        ``else` `if` `((``\$ar``[``\$b``] - ``\$b``) != (``\$ar``[``\$mid``] -``                                        ``\$mid``))``            ``\$a` `= ``\$mid``;``    ``}``    ``return` `(``\$ar``[``\$a``] + 1);``}` `// Driver Code``\$ar` `= ``array``(1, 2, 3, 4, 5, 6, 8 );``\$size` `= sizeof(``\$ar``);``echo` `"Missing number: "``,``     ``search(``\$ar``, ``\$size``);` `// This code is contributed by ajit.``?>`

## Javascript

 ``

Output

`Missing number:7`

Time Complexity: O(log(N)), where N is the length of given array
Auxiliary Space: O(1)

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